Products and Intersections of Prime-Power Ideals in Leavitt Path Algebras
arXiv:2101.05376 · doi:10.1142/S0219498822501043
Abstract
We continue a very fruitful line of inquiry into the multiplicative ideal theory of an arbitrary Leavitt path algebra L. Specifically, we show that factorizations of an ideal in L into irredundant products or intersections of finitely many prime-power ideals are unique, provided that the ideals involved are powers of distinct prime ideals. We also characterize the completely irreducible ideals in L, which turn out to be prime-power ideals of a special type, as well as ideals that can be factored into products or intersections of finitely many completely irreducible ideals.
24 pages. arXiv admin note: text overlap with arXiv:1908.05805